Optimal control of feedback linearizable systems

The authors consider a nonlinear system in which it is desired to minimize a quadratic performance index via smooth state feedback. Such a problem is very difficult to solve exactly via the Euler-Lagrange equations. But, via feedback linearization, the problem can be stated as a linear optimal control problem subject to a nonquadratic performance index. This performance index in the linearizing coordinates is then approximated as a quadratic index, thus obtaining a linear quadratic regulator problem.<
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